Progressive coding of 3D objects based on overcomplete decompositions

This paper presents a progressive coding scheme for 3D objects, based on an overcomplete decomposition of the 3D model on a sphere. Due to increased freedom in the bases construction, redundant expansions have shown interesting approximation properties in the decomposition of signals with multidimensional singularities organized along embedded submanifolds. We propose to map simple 3D models on 2D spheres and then to decompose the signal over a redundant dictionary of oriented and anisotropic atoms that live on the sphere. The signal expansion is computed iteratively with a Matching Pursuit algorithm, which greedily selects the most prominent components of the 3D model. The decomposition therefore inherently represents a progressive stream of atoms, which is advantageously used in the design of scalable representations. An encoder is proposed that compresses the stream of atoms by adaptive coefficient quantization, and entropy coding of atom indexes. Experimental results show that the novel coding strategy outperforms state-of-the-art progressive coders in terms of distortion, mostly at low bit rate. Furthermore, since the dictionary is built on structured atoms, the representation simultaneously offers an increased flexibility. This enables easy stream manipulations, and we finally illustrate this advantage in the design of a view-dependent transmission scheme.